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Patrick had 2,000 ducks and chickens on his farm. He had 3 times as many chickens as ducks. After selling some chickens, he now has twice as many ducks as chickens. How many chickens did he sell?

 
 Sep 8, 2021
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Let Patrick had 'x' number of Ducks.

Since he had 3 times as many chickens as ducks.

∴ Number of chickens Patrick had = 3x

Since he had a total of 2000 Ducks and chickens,

∴ 3x + x = 2000

⇒ 4x = 2000

⇒ x = 500

∴ Number of Ducks Patrick had = 500

And number of Chickens Patrick had = 3x = 3 × 500 = 1500


 


 

 

Now he sells some chicken and after selling he now has twice as many ducks as chickens.

Let he sells 'y' number of chickens,

∴ Number of chickens left = 1500 - y

And the number of Ducks = 500

he now has twice as many ducks as chickens.

∴ 2 × (1500 - y) = 500

⇒ 3000 - 2y = 500

⇒ 2y = 2500

⇒ y = 1250

this means that he sold 1250 chickens.

 

 

 


ANSWER :

Number of chickens Patrick sold = 1250

 
 Sep 8, 2021

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